Displaying similar documents to “Some relations between k-analytic sets and generalized Borel sets”

Non-separable Borel sets

A. H. Stone

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CONTENTS1. Introduction.................................................................................. 32. Baire spaces................................................................................ 53. The basic theorem..................................................................... 94. Cardinality properties; invariance of weight........................... 165. Classification of absolute Borel sets..................................... 226. Characterizations..........................................................................

Borel-Wadge degrees

Alessandro Andretta, Donald A. Martin (2003)

Fundamenta Mathematicae

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Two sets of reals are Borel equivalent if one is the Borel pre-image of the other, and a Borel-Wadge degree is a collection of pairwise Borel equivalent subsets of ℝ. In this note we investigate the structure of Borel-Wadge degrees under the assumption of the Axiom of Determinacy.

A classification of ordinals up to Borel isomorphism

Su Gao, Steve Jackson, Vincent Kieftenbeld (2008)

Fundamenta Mathematicae

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We consider the Borel structures on ordinals generated by their order topologies and provide a complete classification of all ordinals up to Borel isomorphism in ZFC. We also consider the same classification problem in the context of AD and give a partial answer for ordinals ≤ω₂.

Recent developments in the theory of Borel reducibility

Greg Hjorth, Alexander S. Kechris (2001)

Fundamenta Mathematicae

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Let E₀ be the Vitali equivalence relation and E₃ the product of countably many copies of E₀. Two new dichotomy theorems for Borel equivalence relations are proved. First, for any Borel equivalence relation E that is (Borel) reducible to E₃, either E is reducible to E₀ or else E₃ is reducible to E. Second, if E is a Borel equivalence relation induced by a Borel action of a closed subgroup of the infinite symmetric group that admits an invariant metric, then either E is reducible...

Preservation of the Borel class under open-LC functions

Alexey Ostrovsky (2011)

Fundamenta Mathematicae

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Let X be a Borel subset of the Cantor set C of additive or multiplicative class α, and f: X → Y be a continuous function onto Y ⊂ C with compact preimages of points. If the image f(U) of every clopen set U is the intersection of an open and a closed set, then Y is a Borel set of the same class α. This result generalizes similar results for open and closed functions.